We consider an exhaustion of the modular orbifold by compact subsurfaces and show that the growth rate, in terms of word length, of the reciprocal geodesics on such subsurfaces (so named low lying reciprocal geodesics) converges to the growth rate of the full set of reciprocal geodesics on the modular orbifold. We derive a similar result for the low lying geodesics and their growth rate convergence to the growth rate of the full set of closed geodesics
1
CUNY, New York, USA
2
Manhattan College, Riverdale, NY, USA
Ara Basmajian; Robert Suzzi Valli. Combinatorial growth in the modular group. Groups, geometry, and dynamics, Tome 16 (2022) no. 2, pp. 683-703. doi: 10.4171/ggd/667
@article{10_4171_ggd_667,
author = {Ara Basmajian and Robert Suzzi Valli},
title = {Combinatorial growth in the modular group},
journal = {Groups, geometry, and dynamics},
pages = {683--703},
year = {2022},
volume = {16},
number = {2},
doi = {10.4171/ggd/667},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/667/}
}
TY - JOUR
AU - Ara Basmajian
AU - Robert Suzzi Valli
TI - Combinatorial growth in the modular group
JO - Groups, geometry, and dynamics
PY - 2022
SP - 683
EP - 703
VL - 16
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/667/
DO - 10.4171/ggd/667
ID - 10_4171_ggd_667
ER -
%0 Journal Article
%A Ara Basmajian
%A Robert Suzzi Valli
%T Combinatorial growth in the modular group
%J Groups, geometry, and dynamics
%D 2022
%P 683-703
%V 16
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/667/
%R 10.4171/ggd/667
%F 10_4171_ggd_667
